Boltzmann collision operator with inverse-power intermolecular potentials
Boltzmann collision operator with inverse-power intermolecular potentials
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DOI：
10.1002/cpa.3160270406
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发表时间：
2011-08
期刊：
影响因子：
--
通讯作者：
Y. Pao
中科院分区：
文献类型：
--
作者：
Y. Pao
摘要研究了分子间斥力V(r) = a（r sup(- α)）的玻尔兹曼方程中的线性化碰撞算子。证明了碰撞算子具有纯离散谱，其特征函数是无穷可微的(lsup 2)-在（lsup 2）中完全的函数。这个证明依赖于伪微分算子的形式化。报告包括两部分：第一部分讨论了麦克斯韦分子α = 4的特殊情况，而第二部分考虑了α > 2的反幂势的一般情况。(作者)
Abstract : The report studies the linearized collision operator in the Boltzmann equation with repulsive intermolecular potentials V(r) = a(r sup(-alpha)). It is shown that for alpha > 2 the collision operator has a purely discrete spectrum and its eigenfunctions are infinitely differentiable (L sup 2)-functions which are complete in (L sup 2). The proof relies on the formalism of pseudo-differential operators. The report contains two parts: Part I deals with the special case of alpha = 4, the Maxwell's molecules, while Part II considers the general case of inverse-power potentials with alpha > 2. (Author)